On the Viability of Gravitational Bose-Einstein Condensates As

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Hujeirat, ABSTRACT (1) ny pt h oio,btntbeyond. not matter but collapsing distant horizon, the sufficiently the observe to a to up However, able be center. indefinitely would the into observer at collapse dynamical size a small manner undergo quasi-stationary finally a in to contract could star massive counter-balance attraction. could gravitational pressures BH-creation. enormous ther- degenerate the the the the neither nor as self-gravity, mal for principle own their in under framework could collapse stars massive a sufficiently Accordingly, proposed (1931) inevitable are spacetime warped. the BHs solution where indefinitely that This (GR), becomes relativity proof general vacuum. of theoretical in products first field symmetric embedded the M spherically the was mass a for of to solution object corresponds a that equations presented Schwarzschild weak Karl the spacetime. in decoupled, flat conveniently theory LHS in be Newtonian the limit can field volume, the (1) small justifying Eq. accumu- relatively of therefore a RHS strong the in unusually and energy a of is lation there unless Obviously, rmtepito iwo cwrshl’ ouin a solution, Schwarzschild’s of view of point the From Chandrasekar Subrahmanyan later, years Several (1915), in published was GR the thereafter Shortly 1 n ueospeoeai astrophysics in phenomena numerous ing emgei ed httra the thread that fields magnetic he e r on osffro causality a of suffer to found are tes o x-ymti perturbations, axi-symmetric non asstpclfrqaasand quasars for typical masses g onova. euvclypoeteexistence the prove nequivocally yculn ngnrlrelativity. general in coupling gy cetylret unteflow the turn to large fficiently aigsprud ewe two between superfluids tating rscudlo ie therefore like, look could ures i odnae ne normal under condensates nic e hneot MEs as SMBECs) (henceforth tes iy H hudcniu to continue should BHs vity, niedclrto fits of deceleration ensive SA LENTVSTO ALTERNATIVES AS ES nojcs—con- — objects on omlg:dark cosmology: 2

In the early times, this scenario was rejected both by theorists and observers alike and in particular by Einstein and Eddington. Only at the beginning of the sixties the BH-proposal was revived, when BHs appeared to be the only reasonable objects to explain the origin of the vast energy output observed to liberate from quasars. Since then the BH-proposal has been repeatedly adopted and their mass-regime has been continuously expanded to finally span the whole mass spectrum, ranging from the microgram scale up to billion solar Figure 1. The gravitational field of a non-rotating object masses. of mass M embedded in vacuum is equivalent to a curved spacetime having the event horizon as a boundary. The hy- Although BHs are unobservables by definition, the perspace on the right is a projection of the four-dimensional dynamical behavior of matter and stars in their vicinity curved spacetime. in principle should disclose the properties of these objects. In particular, the distinguished depth of their As it will be shown below, the Schwartzschild’s pro- gravitational well, enables BHs to convert a significant posal raises various fundamental questions in GR rather portion of the potential energy of matter or objects than providing a solution to a problem: approaching the BH into other forms of energy, such as The Schwarzschild solution contains two singular- thermal or magnetic energy. In fact there are additional • ities: r=0 and r = r . While the former is in- observational techniques that are used for predicting s trinsic and unremovable, the latter one can be re- the depth of the gravitational well of BHs, e.g., the iron moved by appropriate coordinate transformation, K α emission lines associated with rotating plasmas in e.g. using the Eddington-Finkelstein coordinates accretion disks, the Lorentz factor of ejected plasmas (Hobson et al. 2006). The contraction of the from their vicinity and possibly through gravitational Riemann curvature tensor at the event horizon: waves detectors to be employed in the near future (see R Rµνστ yields a well-defined finite number, Mueller 2007, for additional detection methods). µνστ which implies that the curvature at this radius is well-behaved and that a co-moving observer will Most BHs in binaries are considered to have masses of feel nothing special as she/he crosses the even hori- the order of 10M⊙. The massive ones are generally found zon. at the center of galaxies with masses ranges between sev- In fact it was shown by Penrose (1965) and eral million up to several billions solar masses. In most Hawking (1967) that if Einstein general theory of cases they are observed to be radiatively active, implying relativity is correct and the stress-energy tensor therefore that they are accreting from or ejecting matter satisfies certain positive-definite inqualties, then into their surrounding. spacetime singularities are inevitable. This may Nevertheless, these techniques hint to the existence of imply that all quantum information generally as- objects that differ from normal or compact stars, such sociated with the matter-building the BH will be as old stars, white dwarfs and neutron stars; however completely destroyed. they definitely are unable to determine their nature. Moreover, as the lightcones tend to close up near the event horizon, r = rs, our connection to Difficulties with the classical BH-Proposal observers approaching the event horizon will be continuously weaker and will be completely lost Consider an object of Mass M and spin=0 embed- inside r = rs, which implies that we will never ded in vacuum (see Fig.1), how does the spacetime know if this observer ever crossed the horizon. around this object look like? From the point of view of GR, the equations to be solved This raises a serious question about the progeni- are Gµν =0. tor of BHs. If these were massive stars that run The solution to this problem is a metric, which was out of energy generation via nuclear fusion at their forwarded to Einstein by Schwarzschild just two months centers followed by a dynamical self-collapse under after the former published his theory of GR. The metric their own self-gravity, then from our point of view reads: as distant observers they must be still collapsing and would cross the event horizon with the speed dr2 ds2 =c2(1 r /r)dt2 dΩ¯ 2, (2) of light after infinite time. Equivalently, the pro- − s − 1 r /r − − s genitors of BHs are massive stars that collapsed into rings of matter that surround the event hori- where ds, c, t, rs correspond to the proper distance zon and whose particles approaching the horizon, between two events in this spacetime, the speed of light, but which will never reach or cross it. the time measured by a fixed observer at infinity and 2 the Schwarzschild radius rs = 2GM/c , respectively. A photon of energy E0 = hν0 measured in our The term dΩ¯ 2 =r2dΩ2 =r2(dθ + sin2θ dϕ2) correspond • frame will be infinitely blue-shifted at the event to a differential area on the surface of a sphere of radius r. horizon. Assuming global energy conservation, this indefinite gain of energy must be extracted from 3

the ﬁeld and therefore would cause a non-negligible perturbation to the spacetime. As a consequence, each photon that approaches the horizon will cause a measurable change of spacetime curvature around the BH, which mathematically means, that the solution may not be stable against external perturbations.

The entropy problem of BHs has been investigated Figure 2. The modern picture of a quantum horizon gov- • by Bekenstein (1973), who found that the entropy erned by quantum ﬂuctuations and quantum tunneling, giv- of a BH scales as the number of Planck spheres ing rise to the emission of quanta. The semi-classical ap- accommodate-able within the 2D projection area proach of Hawking predicted that a BH of mass M emits of a BH, or equivalently: BB-radiation at temperature TBB = 1/(8πGM).

rS 2 77 M 2 in complete contradiction to the fundamental prin- S kB( ) kB 10 ( ) . (3) ciples of quantum field theory and in particular to ∼ ℓP ≈ × M⊙ the Heisenberg uncertainty principle (Fig. 2). kB, and ℓP correspond to the Boltzmann constant and the Planck length, respectively. While the progenitors of stellar black hole are well- Assuming a true association of the thermodynam- • understood, the evolution of supermassive black ical variables with the BH thermodynamics, then holes (SMBHs) is still a controversial issue. It is the entropy of progenitor appears to increase by at believed that the Pop III stars in the early universe least twenty orders of magnitude during a transi- must have been sufficiently massive, as the corre- 3 tion into a BH phase. This may imply that a large sponding Jeans mass was of order 10 M⊙ (Bromm amount of information is hidden behind the horizon 1999). and that a deep holographical connection between Such metal-free massive stars must have formed the horizon as a surface and to the BH as bulk is at cosmological redshifts between 8 z 20 and at work (Padmanabhan 2006) should have collapsed relatively fast≤ to≤ form the first massive black holes. Since then their mass The information paradox repeatedly discussed by must have grown exponentially through repeated • theoreticians has not been satisfactorily solved yet. mergers and accretion of matter to acquire typical 9 Noting that the phenomena of particle-wave du- quasar masses of the order 10 M⊙. However, the ality in quantum theory would enable particles to cosmological simulations were able to show certain cross the event horizon as waves, then the informa- condensations of clouds but not the final mass that tion about the pre-collapsed state of matter must exclusively go to form the massive star. In fact be still found in the non-vanishing wave-tail. Such such modeling is associated with various numerical extraction of information is possible due to the uni- difficulties that severely limit the reliability of such tarity requirement of the Hamiltonian operator de- large scale simulations. scribing the quantum state of the infalling particles. However, the only retrievable informations Furthermore, the mass spectrum of BHs suffers of a from BHs is Hawking-quanta, which is of black- gab which ranges from 100 to 10000 M⊙. The origin body type and therefore featureless (s. Fig. 2). of this gab is unclear, especially because this range Similar to the emitted black body radiation from of masses could have been conveniently covered by the sun’s photosphere, these photons transmit the collapse of Pop III type stars. highly diffused information about their paths inside the Sun due to their random-walk motions in optically thick media. Thus the Hawking radiation 2. THE LONG WAY TOWARD BH-ALTERNATIVES carry information about the physical conditions at During the last decade several alternatives to BHs or outside the interface, where they make abrupt have been proposed. A considerable attention was given transition from the opaque spacetime domain in- to dark energy stars (henceforth DESs) and gravitational side the event horizon into the optically thin and vacuum stars (henceforth Gravastars) that have been roughly flat spacetime outside it (s. Preskill 1992, proposed by Chapline et al. (2001); Mazur & Motolla for further details). (2004). Also, it is not clear, whether energy stats of matter Inspired from the Λ cold dark matter cosmology and the behavior of atoms in the vicinity of the − event horizon would obey a Maxwell-Boltzmann (ΛCDM; Peacock 2011)), in which the vacuum en- like-distribution and whether the Planck function ergy is considered to be responsible for the accelerating would continue to properly describe the photon expansion of the universe, one may replace the inner- spectrum. horizon region of a BH by a vacuum-like core or a De Sitter spacetime. The Schwarzschild solution (Eq. 2) unequivocally In this case the effect of gravity is a repulsive rather than • shows, that GR is capable of singling out two events impulsive. As in the case of dark energy in cosmology, the in the spacetime and declare them to be singular in energy density in the core is set to be constant whereas a deterministic manner. However, this approach is the pressure is equal to the negative energy, i.e., P = ρ. − 4

where f(r), and h(r) are metric coefficients to be found. Unlike Newtonian physics in Eucliedian geometry, the distribution of energy in each region may have a significant impact on the curvature of spacetime. Hence a GR-consistent matching procedure, such as the Israel junction condition Israel (1966) is required in order to Figure 3. The gravastar model consists of three sub-domains: construct a global solution that satisfies the conditions a central de Sitter core, a Schwarzschild empty space outside in the three different domains. the object and a thin spherical shell in-between filled with normal matter. One possible solution runs as follows: Such a negative pressure is a typical phenomena on 2 2 the scale of quantum fluctuations as the Casimir-effect In the core region, f(r) = Ch(r) = C (1 H0 r ), • − shows. Furthermore, the equation of state (EoS), P = which is similar to the metric coefficients in the case ρ, is an inevitable consequence of Einstein’s field of de Sitter spacetime in cosmology. The coefficient equations− describing an isotropic and homogeneous uni- H0 is an integration constant that is analogous to verse. Using the Robertson-Walker metric, the Fried- the cosmological Hubble constant, though it has mann equations yield the following evolutionary equation completely different value. for the scaling factor, ”a”: In the outermost region, the solution is identical a¨ 4πG Λ • to that of Schwarzschild, i.e., = (ρ +3p)+ , (4) a − 3 3 r f(r)= h(r)=1 . where Λ denote the cosmological constant anda ¨ cor- − rs responds to the second time derivative of ”a” (see Peacock 2011, for further details). In the intermediate region and in the limit RC • −→ As revealed by cosmological observations, includ- R⋆, the following analytical solution was obtained: ing WMAP and high-redshift Type Ia supernovae 2Gm(r) (Komatsu et al. 2011),a ¨ > 0, which implies that the h(r)=1 ǫ, RHS of Eq. (4) must be positive. However, if vacuum − rc2 ≃ energy density is due to zero-point energy of quantized where m(r) is a continuous mass function, so that fields, then Λ must be a Lorentz invariant and therefore dm(r)=4πρr2dr. ǫ is an integration constant of can be traced back in the history to make it negligibly order the Planck mass MP divided by the mass of small compared to the other terms in the equation. the object. Most importantly, the integration con- Consequently, the term ρ +3P must be negative, hence stant ǫ is strictly positive, which implies that rs is P < ρ/3, or generally, P = ωρ, where ω < 1/3. In − − less than r⋆, therefore prohibiting the formation of fact, recent WMAP cosmological observations reveal an event horizon. a very narrow range for ω : 1.24 ω 0.86 − ≤ ≤ − Following Mazur & Motolla (2004), the thickness (Komatsu et al. 2011), implying therefore that P = ρ of the shell was estimated to be of order: ℓ as EoS for the vacuum core can be safely used. − −14 ∼ √ℓP rs 10 cm, where ℓP is the Planck length. Thus, for≈ a one solar mass gravastar , ℓ would In the case of a Gravastar ((see e.g. Mazur & Motolla hardly exceed the radius of a proton. 2004)), the object consists of the following main three domains (s. Fig. 3): Thus the shell is actually an extremely thin membrane rather than a normal matter-contained shell. Moreover, 1. Region I: 0 r RC , where RC is the core radius. ≤ ≤ the model requires a conversion mechanism of unknown This region is governed by de Sitter spacetime gov- nature to operate efficiently at the base of the mem- erned by the EoS P = ρ. − brane, whose function is to enforce normal matter to undergo a phase transition into a de Sitter vacuum 2. Region III: r > R⋆, where R⋆ is the radius of the (matter) state. object. In this domain Tµν and Λ are set to vanish completely, hence the EoS reads: P = ρ = 0. The reliability of the gravitational Bose-Einstein condensates as BH-alternatives 3. Region II: RC

Table 1 Consider for example the time-evolution of the Different astrophysical objects and their corresponding pressure, P(t), at the center of a neutron star. compactness parameter C. While the dominant contribution is due to the non- thermal degenerate pressure, these objects have still to spend several million years in order to liberate the vast thermal energy trapped in the core 1. While the gravastar model is based on a fluid ap- during the dynamical collapse of the progenitor. A proach, the connection to quantum effects in vac- newly born neutron star is expected to have a cen- 11 12 uum has been performed through the integration tral temperature of TC 10 10 K, but which ≈ − constant ǫ solely, which is rather an ad hoc ap- decreases quickly thereafter to reach several mil- proach. It is unclear, what are those microscopic lion degrees through extensive neutrino emission. quantum effects that would lead to different inte- Without extensive neutrino emission, the stored gration constants for different masses in a universe thermal energy in the core would alter the force of well-defined universal constants. A reasonable balance and may lead to completely different evo- analysis should ensure a scaling out of the depen- lutionary tracks. In particular, the superfluidity dence of ǫ on the mass in order to yield a universal would diminish. constant that applies for a reasonable range of the As the progenitors of a stellar mass Bose-Einstein mass function characterizing astrophysical BHs. condensate (BECs) must be much more massive than that of a NS, the total thermal energy trapped 2. Similarly is the proposed formation of gravitational 2 in the core is of order Vs MBEC, where Vs is Bose-Einstein condensates -GBECs and superflu- the sound speed, assumingU ≈ isothermal core. As this idity of their cores. Although globally stable con- thermal energy would neither disappear in a singu- densates have not been verified experimentally yet, larity, as the case in BHs, nor being expelled to the these are expected to form when the constituents surrounding regions2, must eventually be com- are cooled down to a temperature near absolute U parable to the rest energy of the core. Thus Vs is zero. The particles then congregate into a single relativistic and therefore is much larger than the macroscopic quantum state. In this picture, the su- critical speed, beyond which superfluidity will be perfluid condensate is analogous to a vacuum state, destroyed. Furthermore, as the crust is made of its excited states to normal matter and its surface normal matter, it would serve as source for elec- to a quantum critical shell. Following (Chapline tromagnetic radiation. This loss of energy would 2004), when ordinary particles enter the quantum cause the core to shrink and subsequently collapse critical shell they morph into heavy Bosonic parti- into a BH. cles. We note that in the absence of self-gravity, it In fact, the long time scale of the post-glitch was experimentally verified that external MFs recovery of the Crab and Vela pulsars is a strong tend to shrink the condensates, enhance the self- observational evidence that superfluidity might be interactions and reconnection of vortices and sub- a natural phase governing the flow dynamics in sequently lead to their collapse or explosion as

the cores of relativistic neutron stars. Although 2 the core’s temperature in a NS is of order several Due to the extremely large gravitational redshift 6

bosonova (Wieman et al. 2001). In the case that the BEC-phase is reached via a quasi-stationary contraction of a normal matter core, then the heat capacity of the matter in the crust must have been continuously decreasing to reach a small, but still a positive critical value, below which the BEC would cease to thermally inter- act with the surrounding media. Only a negligibly Figure 4. A frontal crash of a neutron star with a non- rotating supermassive Bose-Einstein condensate. small fraction of ξ = √1 2 of the total internal energy would find its way− outwards,C while the rest is being trapped in the core or diffuses backwards Unless SMBEC are born missive, their cosmolog- from the crust into the core. ical growth will normally be associated with an To conclude: the enormous thermal energy trapped increase of the rotational energy, which enforces in the core during the collapse of the progenitor in the cores to rotate with a speed much higher than combination with magnetic fields and large conver- ΩBEC . sion efficiency of kinetic into thermal energy via Let us now consider the case, in which the core shocks at the surface would eventually act to sup- of the above-mentioned quasar is being hit by a press the superfluidity and superconductivity of the neutron star. Noting that the mean surface den- 2 core and lead to a reverse phase transition. sity of the quasar is: < Σ >BEC = M/(4π rs ) 11 −2 ≈ A further uncertainty of SMBECs is the causality 10 gcm , then the ratio of the surface energy problem. Consider for example the SMBH pow- density of the NS to that of the SMBEC at the ering the high red-shifted quasar PKS 1020-103, time of the crash is: 9 whose mass estimated to be M 2.62 10 M⊙ EΣ and accretion rate of several solar≈ masses× per NS 109. (8) EΣ ≈ year. The light crossing time of this object is BEC τLCT 2 rs/c 7 hours, which is the shortest ∼ ≈ In evaluating the last expression we have assumed possible time scale required for a global re- 6 adjustment of the core to external perturbations. MNS = M⊙ and RNS = 10 cm. On the other hand, for a gravastar, for example, the total mass of the membrane is roughly equal to the Planck mass. Let us consider the case, in which the core con- Thus the mass of the portion of the membrane pos- sists of a single bosonic condensate with a spe- sibly involved directly in this crash can be esti- −21 cific macroscopic quantum state. Unlike white mated to be: MPL (SNS/SSMBEC ) 10 g, dwarfs and neutron stars, in which the Pauli ex- where S✷ means∼ the surface of the corresponding≈ clusion principle prevent their collapse, in the object. Thus, the local energy available for resist- case of boson-like condensates it is the Heisenberg ing the NS-SMBEC crash is of the order of several uncertainty principle that apposes self-collapse. ergs. Also, the local time scale characterizing the −9 The zero-energy state would allow the density of crash event is τLOC RNS/c 10 τGD, where ∼ ≈ bosonic objects to be much larger than in fermionic τGD is the global dynamical time scale of the SM- objects. The critical mass of bosonic objects most 2 BEC. likely obeys the correlation: MCB MP /mB, and Given that the input of energy through the crash 2 2 ∼ MCF M /m for fermionic objects. mB and exceeds the locally available one by several orders ∼ P F mF here denote the mass of an individual bosonic of magnitude and that the NS would crash into and fermionic particles, respectively. Provided that membrane almost with the speed of light, we con- mB is much less than the proton mass, boson ob- clude that a considerable portion of the membrane jects in principle could be much more massive than and the enclosed portion of the SMBEC would be their fermionic counterparts. completely destroyed early enough before the con- If a massive boson condensate consists of one single densate could react dynamically to maintain global vortex line with radius rs and rotational frequency stability. In the case of stellar mass BECs, the in- ΩBEC , then it is easy to verify from the integral of put of energy associated with such a crash would the quantized circulation: destroy the whole condensate. 3. When feeding a gravitational BEC with the mass h V dl = n, rate: M˙ = c3/2G, then the horizon would grow I · 2m with the speed of light. This is equivalent to in- ject the core with one solar mass per 10−5 seconds, −72 M⊙ 3 that: ΩBEC =6 10 ( ) . (7) which is much longer than the duration of a NS- × M BEC SBEC crash-event, which is expected to be of or- Here ”V, l, h, m, n” correspond to the circulation der ǫ (rs/c). Let us assume that the membrane of a velocity, path around the vortex, Planck constant, BEC be located an epsilon small outside the event the mass involved in the vortex core and the horizon, i.e. at rBEC = (1+ ǫ) rs and that this number of vortices, respectively. configuration is applicable to DEOs and indepen- dent of their mass, then it is easy to verify from 7

linearly correlate with the escape velocity, i.e., VJ = α0 Ves, whereat α0 is a constant coeﬃcient of order unity. The Lorentz factor can be expressed then as function of the compactness parameter as follows: Γ = 1/ (1 α2 ). Figure (5) shows that − 0C Γ is highly sensitivep to α0, indicating therefore that large Γ factors between 10 to 20 may be obtained if the− jet velocity is a signiﬁcant fraction of the escape velocity. Equivalently, the jet-plasma must star its outwards-oriented motion from the very vicinity of the object’s surface or from nearly the event horizon.

We note that the formation and acceleration of jet-plasmas around accreting relativistic objects is Figure 5. The Lorentz factor versus the compactness param- considered to be the outcome of complicated cou- eter C is plotted for three different jet launching parameters: 2 pling processes between the accretion disk, the cen- α0 = 1, 0.9, 0.75 denoted with the black, blue and red colors, tral object and the jet-plasma, whereby magnetic respectively. fields play a crucial role (Hujeirat 2004, 2011). the mass-radius relation that: Jets emanating from around surface-free objects dr 2G dM dr are generally observed to be radio-dominated and BEC = (1 + ǫ) > BH . (9) their plasmas propagate with larger Lorentz fac- dt | c2 dt dt | tors compared to those of neutron stars. There- Consequently, in order to ensure that the surface fore, in the case of accreting DEOs the solid sur- of the newly formed core still lays outside the event face in combination with magnetic fields threading horizon, its surface must contradictory grow with the normal-matter-made membrane would give rise a superluminal speed. to an equally significant thermal and radio emission with strong variabilities. These could serve 4. The settling normal matter from the surround- as guide to fix the compactness parameter of the ing would create a multi-component fluid in the object. However, a stellar type DEO would display crust, establishing herewith the appropriate condi- variabilities whose maximum frequency behaves as: tions for the creation of different Fermi surfaces for fermions and bosons and therefore applying a mag- √ c νQP O C . netic tension, which would tend to couple the core ≈ 2π r to the crust dynamically. As a consequence, the If the microquasar GRS 1915+ 105 were a DEO, core break into a multiple number of vortex lines for example, then it would display quasi-periodic threaded by magnetic fields. Similar to the super- oscillation around 400 Hz. This is approximately fluid and superconducting cores in NSs, the vor- one order of magnitude larger than the revealed tex lines in the core of a SMBEC that are coupled value by observations. Moreover, the dominant ra- to the magnetic field would migrate from inside- dio over thermal emission characterizing this ob- to-outside, enhancing thereby self-interaction and jects rules out the possibility of a solid surface. vortex reconnection and diminishing thereby the superfluidity of the core. In this case, we antici- 6. The intensity of the magnetic fields must amplify to pate the surface of a SMBEC to be magnetically reach roughly equipartition values as the accreted active with intense eruption events, though hardly plasma shocks the crust of the SMBEC (Fig. 6). observable. Similar to cores in NSs, the core-crust Consequently, a boundary layer must form, whose coupling through magnetic fields would cause SM- thickness, ℓ, scales as: BEC to decelerate its rotational speed. ℓ V Moreover, we note that rotating superfluids in ( A )2. BEC-cores most likely are similar to rotating super- r⋆ ∼C c fluids between concentric spheres. The latter was verified to be unstable against non-axisymmetric VA in this correlation stands for the Alf`ven speed. perturbations compared to normal rotating Cou- Thus, the boundary layer (BL), which is most likely ette flows (Barenohi & Jones 1987). filled with virially hot elementary particles, is effec- tively a photosphere with a macroscopic thickness 5. Highly collimated relativistic jets have been rather than a membrane with sub-atomic micro- observed to emanate from the vicinity of accreting scopic width. In this case, large scale magnetic BHs and NSs. The Lorentz factors characterizing fields are capable of communicating the presence the propagational speed of these jets were verified of the solid crust to the surrounding media. The to correlate with the compactness parameter freely falling charged particles would then decel- of accreting objects (see Hujeirat et al. 2002, erate in the BL, emitting thereby a considerable 2003, and the references therein). To first order amount of their energy at the synchrotron fre- approximation, we may assume jet-velocities to quency and give rise to a total synchrotron lumi- 8

Such perturbations would enhance the vortex-line migra- tion phenomena, increase their rate of interaction and reconnection and ﬁnally turn the core dissipative, leading subsequently to core collapse into a black hole or explode as bosonova.

Acknowledgments Soﬁe Felhmann (University of Figure 6. Magnetic ﬁelds threading the matter made crust Basel) is greatly acknowledged for reproducing part of (; unscaled thickness) of the condensate. the Figures.

REFERENCES nosity of the order: Alpar, M.A., Sauls, J.A., 1988, ApJ, 327, 723 45 2 M9 3 −1 Barenohi, C.F., Jones, C.A., 1987, Physics Letters A, 8, 122 Lsyn 10 n ( ) erg s . ∼ T4 Bekenstein, J., 1973, ”Black holes and entropy”. Physical Review D 7 (8): 23332346 n, T4,M9 correspond to the number density, the Bromm, V., Coppi, P.S. & Larson, R.B., 1999, ApJ, 527, L5 pre-shock temperature of the accreted plasma and Chapline, G., Hohlfield, E., Laughlin, R.B., 2001, et al., Philos. 9 Mag. B., 81, 235 the mass of the SMBEC in units of 10 M⊙, respec- Chapline, G., 2004, Texas Conference on Relativistic tively. Astrophysics, Stanford, Ca 12/12-12/17/04 Consequently, such a large radio luminosity from a Donley, D.E., Claussen, N.R., Cornish, S.L., et al., Nature 412, geometrically thin BL would be optically thick to 295 synchrotron emission and the BL would appear as Ghezzi, C.R., 2011, Ap&SS, 333, 437 Hawking, S.W., 1967, Proc. R. Soc. London, A300, 187 a bright photospheric ring that surrounds the SM- Hujeirat, A., Camenzind, M., & Livio, M. 2002, A&A, 394, L9 BEC. However, such rings have not been observed Hujeirat, A. 2003, ArXiv Astrophysics e-prints yet, though they would be comfortably observable Hujeirat, A., Livio, M., Camenzind, M., & Burkert, A. 2003, with today’s detectors. A&A, 408 Hujeirat, A. 2004, A&A, 416, 423 Brezinski, F., Hujeirat, A. 2011, Astronomy Studies Development, Vol. 1, No. 1, article e4. 3. SUMMARY Martin, D., Visser, M., 2003, Class. Quantum Grav. 20, 1 Mazur, G., Motolla, E., 2004, Poc. Nat. Acad. Sci., 111, 9546 Various aspects of black holes and dark energy ob- Israel, W., 1966, Nuovo Cimento, 44, 1 jects as BH-candidates have been discussed and the draw Hobson, M.P., Efstathiou, G. & Lasenby A.N., 2006, ”General backs of both kind of objects have been addressed. In Relativity”, Camridge University Press particular, it is argued that gravitational Bose-Einstein Komatsu, E., Smith, K. M., Dunkley, J., & et al., ApJS, 192, 18 condensates, as alternatives to supermassive black holes, Mueller, A., 2007, astro-ph/0701228 Padmanabhan, T., 2006, gr-gc/0606061 suffers of a causal problem and should be ruled out on Peacock, J., book: ”Cosmological Physics”, 2001, CJP the case of merger events. Moreover, the superfluidity Penrose, R., 1965, Phys. Rev. Lett, 14, 57 of SMBEC-cores most likely is a short-living phase and Preskill, 1992, in Intl. Symp. ”Black Holes, Membranes, would not survive non-axisymmetric perturbations initi- Wormholes and Superstings”, hep-th/9209058 ated by the magnetic fields, external forces or mergers.

1 10 1 α2 = 1 0 1-α2C √ 0 α2 = 0.9 0

α2=0.75 0 Γ

0 10 −1 0 10 10 C